EE-194-PLA

Introduction to Plasma Engineering

Part 1: Plasma TechnologyPart 2: Vacuum Basics

Part 3: Plasma Overview

Professor Jeff HopwoodECE Dept., Tufts University

Part 1:Basic Plasma Technology

Plasma: an ionized gas consisting of atoms, electrons, ions, molecules,

molecular fragments, and electronically excited species (informal definition)

www.geo.mtu.edu/weather/aurora/

Plasma: the “fourth state of matter”

solid(ice)

gas(steam)

energy

energyplasma(electrons+ions)

liquid(water)

energy

DC Plasma (AC Fluorescent Lamp…why AC?)

+

- + --

-

+

ArgonElectronArgon ion

Argon + Mercury @ ~0.01 atm.

lamp endcap

--+

--+

--+

--+

--+

- +

”sputtering”

Also, this is the heart of high powered gas lasers.

Fluorescent Lamp SpectrumThe strong peaks of light emission are due to excited Hg:

Hg + e- (hot) Hg* + e-

(cold) Hg + light + e-

http://en.wikipedia.org http://www.chemcool.com

photon

Integrated Circuit Fabricationand Plasma Technology

Microfabricationdeposit-pattern-etch-repeat

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

Copper metallizationon the PowerPC chip

Basic Plasma TechnologySputtering Magnetron

Magnetron

N

S

N

SN

STarget

Substrate

DC

Pulsed

RF

to pump

Basic Plasma TechnologyCapacitively Coupled Plasma

0.4 – 60 MHz

Hopwood and Mantei, JVST A21, S139 (2003)

Plasma Etching

Cl2Cl+ Cl SiCl2

Cl2 SiCl2

Simplified anisotropic etchingCl2 + e- Cl + Cl+ + 2e-

Si(s) + 2Cl(g)+ ion energy SiCl2(g)

S

Anisotropyis due to directional ion bombardment

Cl+Cl

Si(s) + 2Cl(g)+ ion energy SiCl2(g)

The directional ion energy drives the chemical reaction only at the bottom of the microscopic feature.

Dry or Plasma Etching Wet Etching (in acid)

In wet chemistry, the chemical reaction occurs on all surfaces at the same rate. Very small features can not be microfabricated since they eventually overlap each other.

wafer wafer

Jason M. Blackburn, David P. Long, Albertina Cabañas, James J. WatkinsScience 5 October 2001: Vol. 294. no. 5540, pp. 141 - 145

Trenches: etched and filled with copper

Plasma Deposition

SiH4

SiHSiH2H2

SiH4 SiHX+H2

Simplified plasma depositionSiH4 + e- SiH3 + H + e-

SiH3 + e- SiH2 + H + e-

SiH2 + e- SiH + H + e-

SiH + e- Si + H + e-SiHx+ surface+ ion energy Si (s) + Hx(g)

S

Basic Plasma TechnologyElectron Cyclotron Resonance Plasma: Etch and Deposition

Hopwood and Mantei, JVST A21, S139 (2003)

Basic Plasma TechnologyInductively Coupled Plasma: Etch and Deposition

0.4 – 13.56 MHz

Hopwood and Mantei, JVST A21, S139 (2003)

Other applications:Xenon Ion Propulsion

Deep Space 1 encounter with Comet Borrelly

http://nmp.nasa.gov/ds1/images.html

Other Applications :Plasma Display Panels (PDPs)

Structure

From S.S. Yang, et al, IEEE Trans. Plasma Sci. 31, 596 (2003).

red

green

blue

Plasma Display Panels (PDPs)Basic Operation

h ~ 200 ml ~ 400 md ~ 60 m

Sustain Electrode

Bus Electrode

From S.S. Yang, et al, IEEE Trans. Plasma Sci. 31, 596 (2003).

initiate breakdown(~ 300 volts)

+ + + + + +

+ + + +

sustain plasma(~ 180 volts)

surface

Part 2:Basic Vacuum Concepts

Goals

• To review basic vacuum technology– Pressure, pumps, gauges

• To review gas flow and conductance• To understand the flux of vapor phase

material to a substrate• To understand mean free path, l

Ultrahigh Vacuum High Vacuum Rough Vacuum

Typical HighPressure Plasma

Typical Low PressurePlasma Processing

Vacuum (units)

1 atm.1.3x10-31.3x10-61.3x10-9

760 Torr1 Torr1 mTorr1x10-6 Torr

1 Torr =1 mm-Hg

101,333 Pa133 Pa0.133 Pa0.133x10-3 Pa

1 Pascal =1 N/m2

Rough Vacuum• “Mechanical Pumps” typically create a base

pressure of 1-10 mTorr or 0.13-1.3 Pa

Rotary Vane Pump(Campbell)

Warning:Certain process gases are incompatible with pump fluids and pose severe safety risks!

High Vacuum PumpingCryopumps condense gases on cold

surfaces to produce vacuumTypically there are three cold surfaces:(1) Inlet array condenses water and

hydrocarbons (60-100 Kelvin)(2) Condensing array pumps argon,

nitrogen and most other gases (10-20 K)

(3) Adsorption is needed to trap helium, hydrogen and neon in activated carbon at 10-12 K. These gases are pumped very slowly!

Warning: all pumped gases are trapped inside the pump, so explosive, toxicand corrosive gases are not recommended. No mech. pump is needed until regen.

adapted from www.helixtechnology.com

(Campbell)

High Vacuum Pumping

Process chamberTurbomolecular PumpHigh rotation speed turbine imparts momentum to gas atomsInlet pressures: <10 mTorrForeline pressure: < 1 TorrRequires a rough pumpGood choice for toxic and explosive gases – -gases are not trapped in pumpAll gases are pumped at approx. the same ratePumping Speeds:

20 – 2000 liters per sec

foreline

adapted from Lesker.com

High Vacuum PumpingProcess chamber

Heater/Pumping Fluid

Foreline -to mech pump

Diffusion Pump

The process gas is entrained by the downward flow of vaporized pumpingfluid.

Benefits:Low cost, reliable, and rugged.High pumping speed: ~ 2000 l/s

Caution:The process chamber will becontaminated by pumping fluid.A cold trap must be used between thediffusion pump and the process chamber.

Not recommended for “clean” processes.

Water-cooledwalls

adapted from Lesker.com

Flow RateTypically gas flows are cited in units of standard cubic centimeters per minute (sccm) or standard liters per minute (slm)

“Standard” refers to T=273K, P = 1 atm.

Example:Process gas flow of 50 sccm at 5 mTorr (@300K) requires

50 cm-3min-1(760Torr/5x10-3Torr)(300/273)(1min/60sec)(1/103) = 140 liters/sec of pumping speed at the chamber pump port

Conductance Limitation50 sccm

5 mTorr

140 l/s

= Q/(P1 – P2)

Fixed Throughput, Q:Q = 0.005 Torr x 140 l/s = 0.7 Torr-l/s

> 140 l/s …since P2<P1

Conductance depends on geometry and pressure (use tabulated data)

Corifice = ¼ (pa2)<v> l/sCtube = pa2 (2a<v>/3L)

…if mean free path >> a, L(see Mahan, 2000)

Pressure Measurement

Vacuum Gauge Selection adapted from Lesker.com

Convectron Gauge:Initial pumpdown from

1 atm, and as a foreline monitor

Thermal Conductivity of Gas

Baratron:Insensitive to gas

composition,Good choice for

process pressures

True Pressure (diaphragm displacement)

Ion Gauge:Sensitive to gas composition, buta good choice for base pressures

Ionization of Gas

RGA:A simple mass spectrometer

Residual Gas AnalysisLow pressure systems are dominated by water vapor as seen in this RGA of a chamber backfilled with 4x10-5 torr of argonWhy? H2O is a polar molecule that is difficult to pump from the walls --> bake-out the chamber

Source: Pfeiffer vacuum products

Leak?

Gas Density (n)Ideal Gas Law

PV = NkT

Gas density at 1 Pascal at room temp.

N/V = n = P/kT = (1 N/m2)/(1.3807x10-23J/K)(300 K)= [1 (kg-m/s2)/m2]/[4.1x10-21 kg-m2/s2]= 2.4x1020 atoms per m3

= 2.4x1014 cm-3 …at 1 Pa

Rule of Thumb

n(T) = 3.2x1013 cm-3 x (300/T) …at a pressure of 1 mTorr

Gas Kinetics

kTmv

kTm

vvPvf

2exp

24)()(

22/3

2

0

2_ 84)(

mkTdvvvfvcv

vndvvfvnvnZv

zzz 41)( 3

0

Maxwellian Distribution

Average speed of an atom:

Flux of atoms to the x-y plane surface:

(Campbell)Very important!

ExampleA vacuum chamber has a base pressure of 10-6 Torr.

Assuming that this is dominated by water vapor, what is the flux of H2O to a substrate placed in this chamber?

n = 3.2x1013 cm-3/mTorr * 10-3 mTorr = 3.2x1010 cm-3

<v> = (8kT/M)1/2 = 59200 cm/s

z = (¼)n<v> = 4.74x1014 molecules per cm2 per sec!

This is approximately one monolayer of H2O every secondat 10-6 Torr base pressure.

Collisions and Mean Free PathGas Density

n = P/ kT

l 1/sn

Cross-sections ~ d2

d

Rigorous Hard Sphere Collisions: l = kT / 2 d2P

lAr(cm) ~ 8 / P (mTorr)15 22.6 10 cms Ar

Part 3: Plasma Basics

Paschen Curve

http://www.duniway.com/images/pdf/pg/Paschen-Curve.pdf

F. Paschen, Ann. Phys. Chem., Ser. 3 37, 69 (1889). VDC

d

Too few ionizingcollisions: l>d

Too many collisionsElectron energy<ionization energy

What do we need to know about plasma?

substrate

radicals,molecular fragments

ionsWall Wall

gas(ng)

Gas flow

pumping pumping

electronsne, Te

Power

excited atomsand molecules

light

reaction products secondary

electrons

PLASMA

Power Absorbed

substrate

radicals,molecular fragments

ionsWall Wall

gas(ng)

Gas flow

pumping pumping

electronsne, Te

Power

excited atomsand molecules

light

reaction products secondary

electrons

PLASMA

Power Absorbed: DC• DC power

– General electrical mobility and conductivity– Mobility: e = q<t>/m = q/nmme

Where <t> is the average time between collisionsand nm is the collision frequency (collisions per

second)– Electron Conductivity: sDC = qnee = q2ne/nmme

– DC power absorbed: 3)( dvEEP

volDCabs s

Power Absorbed: RF• RF/microwave power

– Ohmic Heating

– Generic electron-neutral collision frequencynm ~ 5x10-8 ngasTe

1/2 (s-1)

… ngas (cm-3), Te(eV).

– Example: Find the pressure at which rf ohmic heating becomes ineffective: nm = 0.1w, Te = 2eV

w = 13.56 MHz * 2 = 85.2Mrad/sngas = 0.1*85.2x106/5x10-8(2)1/2 =

1.2x1014 cm-3 = 3.7 mTorr

VRF

An electron oscillates in a rf electric field without gaining

energyunless

electron collisions occur

3222

2

||21 dvEP

vol m

mDCabs

w

s f=13.56 MHz

Hopwood and Mantei, JVST A21, S139 (2003)

Stochastic Heatingan electron enters and exits a region of high field for a fraction of an rf cycle

t0 << 2/w

Reflecting Boundary (plasma sheath)

-

Emax

E ~ 0

ERF

x

z

vx(t0) > vx(0)

The usual mechanism for heating electrons using RF electric fields at low pressures

Wave/Resonant Heating

x

-Ex

- - -

t1 t2 t3

k

BDC

x

yv

F = q(vxB)

E=0

Electron cyclotron frequency: wce = qB/me = 1.76x107 B(gauss)

If w wce and ERF is perpendicular to BDC, then the electron gains energy from Ex in the absence of collisions.

Ex. f=2.45 GHz --> B=875 G

ERF

W/cm3

Hopwood and Mantei, JVST A21, S139 (2003)

Electron Collisions

substrate

radicals,molecular fragments

ionsWall Wall

gas(ng)

Gas flow

pumping pumping

electronsne, Te

Power

excited atomsand molecules

light

reaction products secondary

electrons

PLASMA

Electron Collisions• Elastic Collisions:

– Ar + e Ar + e– Gas heating: energy is coupled from e to the gas

• Excitation Collisions– Ar + ehot Ar* + ecold, Ar* Ar + hn – Responsible for the characteristic plasma “glow”– Eelectron>Eexc (~11.55 eV for argon)

• Ionization Collisions:– Ar + ehot Ar+ + 2ecold– Couples electrical energy into producing more e_

– Eelectron > Eiz (15.76 eV for argon) • Dissociation:

– O2 + ehot 2O + ecold or O2 + ehot O + O+ + 2ecold– Creates reactive chemical species within the plasma– Eelectron > Ediss (5.12 eV for oxygen)

Collision Cross Sections• Unlike the hard sphere model, real collision cross

sections are a function of electron kinetic energy s(E), or electron velocity s(v).

• We must find the expected collision frequency by averaging over all E or v.

gasgasinelastic nwherenvcm

cmvt

slsl

/1...)(

sec)/(1

vK

dvvfvvnvn gasgasinelastic

s

ss0

)()(

becomes

(cm3s-1)

Graphicallyf(E

) or s

(E)

Electron energy, E

sAr(E)

f(E)

Te Eiz

Note: the exponential tail of energeticelectrons is responsible for ionization

The RATE CONSTANT: Kiz(Te) Kizoexp(-Eizo/Te)

curve fitting

Graphicallyf(E

) or s

(E)

Electron energy, E

sAr(E)

f(E)

Te Eiz

Note: the exponential tail of energeticelectrons is responsible for ionization

The RATE CONSTANT: Kiz(Te) Kizoexp(-Eizo/Te)

curve fitting

Hot electrons – more ionization

Examples of Numerically Determined Rate Constants (Lieberman, 2005)

Generation Rate of Plasma Species by Electron Collisions

y + e x + ednx/dt = Kxneny

For example,

Ar + e Ar+ + e + edne/dt = Kiznengas

is the number of electrons (and ions) generated per cm3 per second

Electron-Ion RecombinationThree-Body Problem: e + Ar+ + M Ar + M the third body is needed to conserve energy and momentum in the recombination process

-

+

MM

-

+M

wall recombination dominates at low pressure because three body collisions are rare

wall recombination volume recombination

Transport to Surfaces

substrate

radicals,molecular fragments

ionsWall Wall

gas(ng)

Gas flow

pumping pumping

electronsne, Te

Power

excited atomsand molecules

light

reaction products secondary

electrons

PLASMA

n = ¼ n<v>

neni

r 0

Electron and Ion Loss to the Substrate and Walls- the plasma sheath -

electrons are much more mobile than ionse = q<t>/me >> q<ti>/mi = i

neni

r 0neni

r 0

-

-

- - --

-

-- --

chamber

Electron and Ion Loss to the Substrate and Walls- the plasma sheath -

r(x)

x

+ +

ne = ni

ne<<ni(sheath)

x

V(x) e

(after Mahan, 2000)

-1kV

s

x

V

0 v

+

low energy electrons are trapped within the plasma, but ions are accelerated by the sheath potential to the chamber walls and substrate

Ion FluxThe ion flux to a solid object is determined by

the Bohm velocity (or sound speed) of the ion:

uB = (kTe/mi)1/2 = 9.8x105 (Te/M)1/2 cm/s

=9.8x105 (3 eV/40 amu)1/2 ~ 2.5x105 cm/s

…and the ion flux is given by i = uBni (cm-2s-1)

(this is the ion speed at the edge of the sheath)

Electron Flux• Only the most energetic electrons can

overcome the sheath potential, Vs.• e = ¼ ne<ve> exp (qVs/kTe)

f(E)

Electron energy, E Te qVs

flux to surface Boltzmann factor

Sheath Potential, Vs

In the steady state, the electron and ion fluxes to the chamber/substrate must be equal, if there is no external current path

e = i

¼ ne<ve> exp (qVs/kTe) = uBni = (kTe/mi)1/2 negiving

Vs = -Teln(mi/2me) ~ -5Te

This is often called the floating potential: Isolated surfaces have a negative potential relative to the plasma.

Ion Energy

(after Mahan, 2000)

-1kV

s

x

V

0 v

Ex: Assuming argon with Te = 3 eV,

the ion energy at the cathode is Ei = q(1 kV + 4.7Te) = 1014 eV

ignoring ion-neutral collision within s,and the ion energy at the anode is Ei = 4.7 Te = 14 eV

Ion mean free path:li = 1/ngassi ~ 3/p (cm) for Ar+

…where p is the pressure in mTorrHere li = 3/100 cm or 0.3 mm @ 0.1 torr

NOTE: s>>li Ei << 1014 eV!

Particle Conservationand Electron Temperature

A simple model for electron temperature can be found for a steady state plasma:

# of ions created/sec = # of ions lost/secKizngasneV = uBniAeff

Kiz/uB = Kizoe-Eiz/kTe /(kTe/mi)1/2 = Aeff/(V ngas)=1/deffngas

(V=plasma volume, Aeff = effective chamber area, deff = V/Aeff)

ne=ni

The electron temperature (Te) is a unique function of

1. gas density, ngas (pressure)

2. chamber size, deff = V/Aeff

3. gas type: Kiz, Eiz

Single-step vs. Two-step Ionization

ngdeff (m-2)

1e+18 1e+19 1e+20 1e+21 1e+22

Te (e

V)

0

1

2

3

4

5

6

7

n0 = 1 x 1011 cm-3

single-step

two-step

Ar+eAr*+eAr* + e Ar+ + 2e

Ar + e Ar+ + 2eExample:Two large parallel plates separated by 2 cm are used to sustain an argon plasma at 25 mTorr. Find Te.

deff = V/Aeff ~ R2d / (R2 +R2) = d/2

ngasdeff ~ (25*3.2x1019m-3)(0.01m) =0.8e+19 m-2

Te = 3 eV

(Note: we have assume that the plasma density is uniform)

Power Conservation and Electron Density, ne

Power Absorbed by the Plasma = Power Lost from the Plasma

Pabs = [qniuBEion+q(¼ne<ve>eVs/kTe )Eelec]Aeff +(Pheat+Plight+Pdiss)

≡ qneuBAeff(Eion + Eelec + Ec)

where EC is the collisional energy lost in creating an electron-ion pair due to ionization, light, dissociative

collisions, and heat:EC = [nizEiz + nexEex + ndissEdiss + nm(3me/mi)Te]/niz

qVs2Te

Pion Pelectron

Te (eV)

2 3 4 5 6 7 8 91 10

E L (eV

)

101

102

103

104

N2

Ar

C

Collisional Energy Loss

Electron Density ExampleContinuing with the previous example

A plasma is sustained in argon at 25 mTorr between two parallel plates separated by 2 cm. The radius of the plates is 20 cm and the power absorbed by the plasma is 100 watts. Find ne.

100 W = qneuBAeff(Eion + Eelec + Ec)= (1.6x10-19C)ne(2.5x105cm/s)(2x202 cm2)

x(5Te + 2Te + 35 eV)

ne = 1.3x1010 cm-3

Find ne if the gas is N2, assuming that Te ~ 3 eV

100 W = (1.6x10-19C)ne(2.5x105cm/s)(2x202 cm2)(5Te + 2Te + 400 eV)

ne = 2.3 x 109 cm-3

Example (cont’d)Repeat the previous example using argon, BUT include an electrode voltage of 1000v that is applied to one plate to sustain the plasma.

100 W = qneuBAeff(Eion + Eelec + Ec)= (1.6x10-19C)ne(2.5x105cm/s)(x202 cm2) x

{(5Te + 2Te + 35 eV)+[(1000 eV+5Te) + 2Te + 35 eV]}

ne = 1.7x109 cm-3

anode cathode

Secondary Electronse = gsec i , where gsec~0.1-10 and Ee ~ qVs

substrate

radicals,molecular fragments

ionsWall Wall

gas(ng)

Gas flow

pumping pumping

electronsne, Te

Power

excited atomsand molecules

light

reaction products secondary

electrons

PLASMA

secondaryelectrons

Summary

substrate

radicals,molecular fragments

ionsWall Wall

gas(ng)

Gas flow

pumping pumping

electronsne, Te

Power

excited atomsand molecules

light

reaction products secondary

electrons

PLASMA

Conclusion• Basics of Vacuum

– ng, <v>, n,, l• Plasma Generation and Simple Models

– Te, ne, ni, i • Basic Plasma Generation

– DC (sputter deposition systems)– AC < 400 kHz (plasma displays, lighting)– Radio Frequency 0.4<f<900 MHz (etching and

deposition)– Microwave > 900 MHz